1. Field of the Invention
The present invention relates to the correction of artifacts in computed tomography and, in particular, to the correction of artifacts in helical multi-slice computed tomography.
2. Description of the Related Art
Commonly existing single slice CT systems employ an array of x-ray detectors which extend a line or an arc in the transverse plane (the transverse plane is also called the scan plane or the X-Y plane). The x-ray source is collimated in such a way as to limit the x-ray radiation only to the detector array. As a result of this geometry, in the static scan mode the data collected by the detector array during one revolution of the x-ray source and the x-ray detectors pertains to one plane which is defined by the x-ray focal spot and the array of detectors, and the ensuing image shows a cut through the scanned object at this same plane.
In the helical scan mode, the object moves in the axial direction during the scan, so that the data collected during the scan corresponds to longer axial length, however the data is still collected along the same plane in space, although the object is now in motion relative to this plane.
In order to speed up the process of data collection, x-ray CT cone beam multi-slice systems were developed having multi-slice arrangement of detectors. This multi-slice arrangement of detectors can be obtained by actually stacking several layers of detector arrays in the axial direction, or by using other area detectors such as x-ray image intensifier and more. The x-ray source is now collimated as to allow the x-ray radiation to be collected by all the area of detector arrays thus covering a larger volume than in the case of single slice systems. Multi-slice scanners can be used in the static mode, covering larger volume in one scan, but their largest advantage is achieved in helical scans where the gain in the speed along the axial direction will be proportional to the number of slices.
The "cone beam" part in the name of the described systems refers to the fact that radiation of the x-ray source extends a cone-like portion of space, or in other words, the radiation diverges from one spot. Consequently, the planes defined by the different detector arrays and the focal spot (detection planes), are not parallel to each other, but also converge towards the x-ray focal spot.
The last fact, the convergence of the detection planes, is currently a weakness of x-ray CT cone beam multi-slice systems, because images generated with the commonly available reconstruction algorithms sometimes result in several types of artifacts in the images. One of the ways to reduce those artifacts is the generation of finite width images which are processed by filtered interpolation. The complimentary data rebinning is used, both in the regular generation of zero width images or in the generation of finite width images, in order to improve the spatial resolution in the axial direction. However the addition of the complimentary data results in artifacts.
To better illustrate how these artifacts arise, it is useful to consider multi-slice image generation. In fan beam multi-slice CT, the reconstruction of an image is typically preceded by slice data generation (SLG). The slice data (SD) generated at this stage is a set of data which is designed to approximate a set of two dimensional data that would have been collected in a stationary two dimensional scan at a specific image plane. Consequently the SD are arranged in SD fan-views which are generated from the acquisition data, better known as projection data, which is the acquired data after the necessary corrections and processing. The acquisition data belonging to every detector line are arranged in acquisition fan-views, where each acquisition fan-view contains one data point corresponding to each channel, ordered according to channel numbers or channel angles. All these data points within an acquisition fan-view are acquired at the same time, and therefore have the same axial position which depends on the view angle. The axial position assigned to all the points (regardless of channel number) within an acquisition fan view V.sub.n, with fan-view angle .alpha..sub.n, and acquired by detector line k, is given by the following expression: ##EQU1## where P is the helical pitch, which is the axial distance traveled by the scanned object during one full rotation (360 degrees) of the x-ray tube, and Z.sub.0k is the initial (at the beginning of the rotation) axial position of the kth detector line.
The fact that the SD is designed to approximate the data that would have been collected in a stationary two-dimensional scan at a specific user-determined axial position, and, on the other hand, each acquisition fan-view corresponds to a different axial position, explains why some interpolation processing with respect to the axial direction is required.
The interpolation processing can be simple linear interpolation, or higher order interpolation, when the reconstructed image plane is a thin plane (zero reconstruction width) defined by one point on the Z axis, or it can be filtered interpolation processing (discrete filtering or continuous filtering), when the reconstructed image plane is thick and defined by its center and its reconstruction width. As a concrete example, the description will concentrate on linear interpolation in the generation of thin slices, but the treatment of the other cases can be derived from the same principles. For example, in the case of the discrete filtering, the same description applies to each of the thin slices involved in the filtering, and the same correction has to be applied to each of these thin slices.
As explained above, when only direct data is involved in the SLG, all the acquisition data points in each acquisition fan-view, or SD fan-view, correspond to the same axial position, irrespective of the channel number. The situation is more complicated when complementary data (reflection data, or opposite data) are incorporated in the SLG. As each direct data point involved in the SLG can be characterized by belonging to detector line k, fan-view V.sub.n with fan angle .alpha..sub.n, and channel angle .beta..sub.m, the corresponding complementary data point is then defined as belonging to the same detector line k, with opposite channel angle -.beta..sub.m, and belonging to an acquisition fan-view defined by its angle as .alpha..sub.n +2.beta..sub.m +.pi.. This transformation from direct data point to its complimentary data point can be summarized: EQU (.alpha..sub.n, .beta..sub.m).fwdarw.(.alpha..sub.n +2.beta..sub.m +.pi., -.beta..sub.m)
The last result shows that the complimentary data points involved in the generation of the SD at a specific SD fan-view, belongs to many different acquisition fan-views, and therefore these points correspond to different axial positions. The fact that in general the new fan-view angles do not correspond to real acquisition fan-view angles is corrected by interpolation using the real acquisition fan-views.
To understand how these facts result in a discontinuity refer to FIG. 1, which shows the axial positions of the acquisition data points under consideration as a function of the SD view number, or view angle. The graphical consequence of the constant axial motion, the fact that the acquisition data points within a fan-view are all taken at the same time, and the fact that the acquisition fan-view are collected in succession in time is that the lines representing the positions are tilted with a constant slope with respect to the axial position and view angle axes. This slope is determined by Equation 1 given above. The full lines represent the positions of the direct data D1, D2, and D3, for all channel numbers, and the broken lines which are tilted with the same slope, correspond to the positions of the complimentary data points. Contrary to the direct data lines, each channel number is represented by a different broken line. Consequently the broken line denoted by C(n1) corresponds to a certain channel number n1, and the broken line denoted by C(n2) corresponds to another channel number n2. More generally, the dependence of the axial position of the complimentary points belonging to one acquisition fan view (and one detector segment) on their channel number, is linear dependence. This dependence can be described as motion with respect to the axial position of the direct data points in the same view which do not depend on the channel number and therefor do not move. At certain scan parameters the position of the opposite data can cross over the position of the direct data. The channel at which this cross-over occurs is a point of discontinuity in the slice data. For the purpose of this demonstration, the axial positions of the data points will be denoted as Z(D1), Z(D2), and Z(D3), for the direct data D1, D2, and D3, respectively, and Z(n1), and Z(n2) for the complimentary points, C(n1) and C(n2). The vertical line is drawn at the axial position Z, of the image plane, and the intersection of this line with the horizontal line that is drawn through V1, determines the interpolation point for all the channels in view V1. Since the positions of the data points depend on the channel number, the interpolation operation also depends on the channel number.
For channel n1 the result of the calculated value D(Z,V1,n1) is obtained by linear interpolation with D1 and C1-D(Z,V1,n1)=LI(Z(D1),Z(n1),Z,D1,C(n1)), where LI is the linear interpolation operation. The first step implied by the equation above is the identification of Z(D1) and Z(n1) as the two closest neighbor points on both sides of Z, and the application of the linear interpolation, follows as the second step: ##EQU2## where x1 and x2 are, by definition, the closest points on both sides of point x, and D1 and D2 are the data corresponding to them.
For channel n2 the result of the calculated value D(Z,V1,n2) is obtained by linear interpolation with D1 and D2-D(Z,V1,n2)=LI(Z(D1),Z(D2),Z,D1,D2).
Here, in the calculation for n2, the two points on both sides of Z are Z(D1) and Z(D2), the reason being that at some intermediate point between n1 and n2, the line representing the axial position of the complimentary data points crossed the line of the direct data point Z(D2).
Denoting now
I1(ni)=D(z,v1,ni) for ni&lt;n1 and, PA1 I2(nj)=D(z,v1,nj) for nj&gt;n2, PA1 it can be seen that the difference between the result for I1 and the result for I2 is that, I1 (an interpolated set of data) depends on complimentary value C(n1), while I2 (another interpolated set of data) depends in the same way on D2. Due to the cone angle, data value D2 and data value C(n1) may not belong to the same detector angle and they are generally not equal, so that the data obtained in I2 is not a smooth continuation of the data obtained by I1. The occurrence of the discontinuity between I1 and I2 is shown in FIG. 2, which shows the two sets of calculated values as a function of the channel number. This manifests itself as streaks in a high density object in the image. The problem is that I1 is performed for some range of channels n where n&lt;n1, and I2 is performed for some range channels n where n&gt;n2.